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  <h1>Source code for describe.descriptors.matrixdescriptor</h1><div class="highlight"><pre>
<span></span><span class="kn">from</span> <span class="nn">__future__</span> <span class="k">import</span> <span class="n">absolute_import</span><span class="p">,</span> <span class="n">division</span><span class="p">,</span> <span class="n">print_function</span><span class="p">,</span> <span class="n">unicode_literals</span>
<span class="kn">from</span> <span class="nn">builtins</span> <span class="k">import</span> <span class="p">(</span><span class="nb">bytes</span><span class="p">,</span> <span class="nb">str</span><span class="p">,</span> <span class="nb">open</span><span class="p">,</span> <span class="nb">super</span><span class="p">,</span> <span class="nb">range</span><span class="p">,</span>
                      <span class="nb">zip</span><span class="p">,</span> <span class="nb">round</span><span class="p">,</span> <span class="nb">input</span><span class="p">,</span> <span class="nb">int</span><span class="p">,</span> <span class="nb">pow</span><span class="p">,</span> <span class="nb">object</span><span class="p">)</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">from</span> <span class="nn">describe.descriptors</span> <span class="k">import</span> <span class="n">Descriptor</span>


<div class="viewcode-block" id="MatrixDescriptor"><a class="viewcode-back" href="../../../doc/describe.descriptors.html#describe.descriptors.matrixdescriptor.MatrixDescriptor">[docs]</a><span class="k">class</span> <span class="nc">MatrixDescriptor</span><span class="p">(</span><span class="n">Descriptor</span><span class="p">):</span>
    <span class="sd">&quot;&quot;&quot;A common base class for two-body matrix-like descriptors.</span>
<span class="sd">    &quot;&quot;&quot;</span>
    <span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">n_atoms_max</span><span class="p">,</span> <span class="n">permutation</span><span class="o">=</span><span class="s2">&quot;sorted_l2&quot;</span><span class="p">,</span> <span class="n">sigma</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">flatten</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
        <span class="sd">&quot;&quot;&quot;</span>
<span class="sd">        Args:</span>
<span class="sd">            n_atoms_max (int): The maximum nuber of atoms that any of the</span>
<span class="sd">                samples can have. This controls how much zeros need to be</span>
<span class="sd">                padded to the final result.</span>
<span class="sd">            permutation (string): Defines the method for handling permutational</span>
<span class="sd">                invariance. Can be one of the following:</span>
<span class="sd">                    - none: The matrix is returned in the order defined by the Atoms.</span>
<span class="sd">                    - sorted_l2: The rows and columns are sorted by the L2 norm.</span>
<span class="sd">                    - eigenspectrum: Only the eigenvalues are returned sorted</span>
<span class="sd">                      by their absolute value in descending order.</span>
<span class="sd">                    - random: ?</span>
<span class="sd">            sigma (float): Width of gaussian distributed noise determining how much the</span>
<span class="sd">                rows and columns of the randomly sorted coulomb matrix are scrambled.</span>
<span class="sd">            flatten (bool): Whether the output of create() should be flattened</span>
<span class="sd">                to a 1D array.</span>
<span class="sd">        &quot;&quot;&quot;</span>
        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="n">flatten</span><span class="p">)</span>

        <span class="c1"># Check parameter validity</span>
        <span class="k">if</span> <span class="n">n_atoms_max</span> <span class="o">&lt;=</span> <span class="mi">0</span><span class="p">:</span>
            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span>
                <span class="s2">&quot;The maximum number of atoms must be a positive number.&quot;</span>
            <span class="p">)</span>
        <span class="n">perm_options</span> <span class="o">=</span> <span class="nb">set</span><span class="p">((</span><span class="s2">&quot;sorted_l2&quot;</span><span class="p">,</span> <span class="s2">&quot;none&quot;</span><span class="p">,</span> <span class="s2">&quot;eigenspectrum&quot;</span><span class="p">,</span> <span class="s2">&quot;eigenspectrum&quot;</span><span class="p">,</span> <span class="s2">&quot;random&quot;</span><span class="p">))</span>
        <span class="k">if</span> <span class="n">permutation</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">perm_options</span><span class="p">:</span>
            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span>
                <span class="s2">&quot;Unknown permutation option given. Please use one of the following: </span><span class="si">{}</span><span class="s2">.&quot;</span>
                <span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="s2">&quot;, &quot;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">perm_options</span><span class="p">))</span>
            <span class="p">)</span>

        <span class="k">if</span> <span class="ow">not</span> <span class="n">sigma</span> <span class="ow">and</span> <span class="n">permutation</span> <span class="o">==</span> <span class="s1">&#39;random&#39;</span><span class="p">:</span>
            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span>
                <span class="s2">&quot;Please specify sigma as a degree of random noise.&quot;</span>
            <span class="p">)</span>

        <span class="bp">self</span><span class="o">.</span><span class="n">n_atoms_max</span> <span class="o">=</span> <span class="n">n_atoms_max</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">permutation</span> <span class="o">=</span> <span class="n">permutation</span>
        <span class="bp">self</span><span class="o">.</span><span class="n">norm_vector</span> <span class="o">=</span> <span class="kc">None</span>

<div class="viewcode-block" id="MatrixDescriptor.describe"><a class="viewcode-back" href="../../../doc/describe.descriptors.html#describe.descriptors.matrixdescriptor.MatrixDescriptor.describe">[docs]</a>    <span class="k">def</span> <span class="nf">describe</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">system</span><span class="p">):</span>
        <span class="sd">&quot;&quot;&quot;</span>
<span class="sd">        Args:</span>
<span class="sd">            system (System): Input system.</span>

<span class="sd">        Returns:</span>
<span class="sd">            ndarray: The zero padded Coulomb matrix either as a 2D array or as</span>
<span class="sd">                a 1D array depending on the setting self.flatten.</span>
<span class="sd">        &quot;&quot;&quot;</span>
        <span class="n">matrix</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_matrix</span><span class="p">(</span><span class="n">system</span><span class="p">)</span>

        <span class="c1"># Handle the permutation option</span>
        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">permutation</span> <span class="o">==</span> <span class="s2">&quot;none&quot;</span><span class="p">:</span>
            <span class="k">pass</span>
        <span class="k">elif</span> <span class="bp">self</span><span class="o">.</span><span class="n">permutation</span> <span class="o">==</span> <span class="s2">&quot;sorted_l2&quot;</span><span class="p">:</span>
            <span class="n">matrix</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">sort</span><span class="p">(</span><span class="n">matrix</span><span class="p">)</span>
        <span class="k">elif</span> <span class="bp">self</span><span class="o">.</span><span class="n">permutation</span> <span class="o">==</span> <span class="s2">&quot;eigenspectrum&quot;</span><span class="p">:</span>
            <span class="n">matrix</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_eigenspectrum</span><span class="p">(</span><span class="n">matrix</span><span class="p">)</span>
        <span class="k">elif</span> <span class="bp">self</span><span class="o">.</span><span class="n">permutation</span> <span class="o">==</span> <span class="s2">&quot;random&quot;</span><span class="p">:</span>
            <span class="n">matrix</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">sort_randomly</span><span class="p">(</span><span class="n">matrix</span><span class="p">)</span>
        <span class="k">else</span><span class="p">:</span>
            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span>
                <span class="s2">&quot;Invalid permutation method: </span><span class="si">{}</span><span class="s2">&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">permutation</span><span class="p">)</span>
            <span class="p">)</span>

        <span class="c1"># Add zero padding</span>
        <span class="n">matrix</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">zero_pad</span><span class="p">(</span><span class="n">matrix</span><span class="p">)</span>

        <span class="c1"># Flatten the matrix if requested</span>
        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">flatten</span><span class="p">:</span>
            <span class="n">matrix</span> <span class="o">=</span> <span class="n">matrix</span><span class="o">.</span><span class="n">flatten</span><span class="p">()</span>

        <span class="k">return</span> <span class="n">matrix</span></div>

<div class="viewcode-block" id="MatrixDescriptor.sort"><a class="viewcode-back" href="../../../doc/describe.descriptors.html#describe.descriptors.matrixdescriptor.MatrixDescriptor.sort">[docs]</a>    <span class="k">def</span> <span class="nf">sort</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">matrix</span><span class="p">):</span>
        <span class="sd">&quot;&quot;&quot;Sorts the given matrix by using the L2 norm.</span>

<span class="sd">        Args:</span>
<span class="sd">            matrix(np.ndarray): The matrix to sort.</span>

<span class="sd">        Returns:</span>
<span class="sd">            np.ndarray: The sorted matrix.</span>
<span class="sd">        &quot;&quot;&quot;</span>
        <span class="c1"># Sort the atoms such that the norms of the rows are in descending</span>
        <span class="c1"># order</span>
        <span class="n">norms</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">norm</span><span class="p">(</span><span class="n">matrix</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
        <span class="n">sorted_indices</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">argsort</span><span class="p">(</span><span class="n">norms</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)[::</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
        <span class="n">sorted_matrix</span> <span class="o">=</span> <span class="n">matrix</span><span class="p">[</span><span class="n">sorted_indices</span><span class="p">]</span>
        <span class="n">sorted_matrix</span> <span class="o">=</span> <span class="n">sorted_matrix</span><span class="p">[:,</span> <span class="n">sorted_indices</span><span class="p">]</span>

        <span class="k">return</span> <span class="n">sorted_matrix</span></div>

<div class="viewcode-block" id="MatrixDescriptor.get_eigenspectrum"><a class="viewcode-back" href="../../../doc/describe.descriptors.html#describe.descriptors.matrixdescriptor.MatrixDescriptor.get_eigenspectrum">[docs]</a>    <span class="k">def</span> <span class="nf">get_eigenspectrum</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">matrix</span><span class="p">):</span>
        <span class="sd">&quot;&quot;&quot;Calculates the eigenvalues of the matrix and returns a list of them</span>
<span class="sd">        sorted by their descending absolute value.</span>

<span class="sd">        Args:</span>
<span class="sd">            matrix(np.ndarray): The matrix to sort.</span>

<span class="sd">        Returns:</span>
<span class="sd">            np.ndarray: A list of eigenvalues sorted by absolute value.</span>
<span class="sd">        &quot;&quot;&quot;</span>
        <span class="c1"># Calculate eigenvalues</span>
        <span class="n">eigenvalues</span><span class="p">,</span> <span class="n">_</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">eig</span><span class="p">(</span><span class="n">matrix</span><span class="p">)</span>

        <span class="c1"># Remove sign</span>
        <span class="n">abs_values</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">absolute</span><span class="p">(</span><span class="n">eigenvalues</span><span class="p">)</span>

        <span class="c1"># Get ordering that sorts the values by absolute value</span>
        <span class="n">sorted_indices</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">argsort</span><span class="p">(</span><span class="n">abs_values</span><span class="p">)[::</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>  <span class="c1"># This sorts the list in descending order in place</span>
        <span class="n">eigenvalues</span> <span class="o">=</span> <span class="n">eigenvalues</span><span class="p">[</span><span class="n">sorted_indices</span><span class="p">]</span>

        <span class="k">return</span> <span class="n">eigenvalues</span></div>

<div class="viewcode-block" id="MatrixDescriptor.zero_pad"><a class="viewcode-back" href="../../../doc/describe.descriptors.html#describe.descriptors.matrixdescriptor.MatrixDescriptor.zero_pad">[docs]</a>    <span class="k">def</span> <span class="nf">zero_pad</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">array</span><span class="p">):</span>
        <span class="sd">&quot;&quot;&quot;Zero-pads the given matrix.</span>

<span class="sd">        Args:</span>
<span class="sd">            array (np.ndarray): The array to pad</span>

<span class="sd">        Returns:</span>
<span class="sd">            np.ndarray: The zero-padded array.</span>
<span class="sd">        &quot;&quot;&quot;</span>
        <span class="c1"># Pad with zeros</span>
        <span class="n">n_atoms</span> <span class="o">=</span> <span class="n">array</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
        <span class="n">n_dim</span> <span class="o">=</span> <span class="n">array</span><span class="o">.</span><span class="n">ndim</span>
        <span class="n">padded</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">pad</span><span class="p">(</span><span class="n">array</span><span class="p">,</span> <span class="p">[(</span><span class="mi">0</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">n_atoms_max</span><span class="o">-</span><span class="n">n_atoms</span><span class="p">)]</span><span class="o">*</span><span class="n">n_dim</span><span class="p">,</span> <span class="s1">&#39;constant&#39;</span><span class="p">)</span>

        <span class="k">return</span> <span class="n">padded</span></div>

<div class="viewcode-block" id="MatrixDescriptor.get_number_of_features"><a class="viewcode-back" href="../../../doc/describe.descriptors.html#describe.descriptors.matrixdescriptor.MatrixDescriptor.get_number_of_features">[docs]</a>    <span class="k">def</span> <span class="nf">get_number_of_features</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
        <span class="sd">&quot;&quot;&quot;Used to inquire the final number of features that this descriptor</span>
<span class="sd">        will have.</span>

<span class="sd">        Returns:</span>
<span class="sd">            int: Number of features for this descriptor.</span>
<span class="sd">        &quot;&quot;&quot;</span>
        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">permutation</span> <span class="o">==</span> <span class="s2">&quot;eigenspectrum&quot;</span><span class="p">:</span>
            <span class="k">return</span> <span class="nb">int</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">n_atoms_max</span><span class="p">)</span>
        <span class="k">else</span><span class="p">:</span>
            <span class="k">return</span> <span class="nb">int</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">n_atoms_max</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span></div>

<div class="viewcode-block" id="MatrixDescriptor.sort_randomly"><a class="viewcode-back" href="../../../doc/describe.descriptors.html#describe.descriptors.matrixdescriptor.MatrixDescriptor.sort_randomly">[docs]</a>    <span class="k">def</span> <span class="nf">sort_randomly</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">matrix</span><span class="p">,</span> <span class="n">sigma</span><span class="o">=</span><span class="mi">1</span><span class="p">):</span>
        <span class="sd">&quot;&quot;&quot;</span>
<span class="sd">        Given a coulomb matrix, it adds random noise to the sorting defined by sigma.</span>
<span class="sd">        For sorting, L2-norm is used</span>

<span class="sd">        Args:</span>
<span class="sd">            matrix(np.ndarray): The matrix to randomly sort.</span>

<span class="sd">        sigma:</span>
<span class="sd">            float: Width of gaussian distributed noise determining how much the</span>
<span class="sd">                rows and columns of the randomly sorted coulomb matrix are scrambled.</span>

<span class="sd">        Returns:</span>
<span class="sd">            np.ndarray: The randomly sorted matrix.</span>

<span class="sd">        &quot;&quot;&quot;</span>
        <span class="k">try</span><span class="p">:</span>
            <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">norm_vector</span><span class="p">)</span>
        <span class="k">except</span><span class="p">:</span>
            <span class="bp">self</span><span class="o">.</span><span class="n">_get_norm_vector</span><span class="p">(</span><span class="n">matrix</span><span class="p">)</span>

        <span class="n">noise_norm_vector</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">norm_vector</span><span class="p">,</span> <span class="n">sigma</span><span class="p">)</span>
        <span class="n">indexlist</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">argsort</span><span class="p">(</span><span class="n">noise_norm_vector</span><span class="p">)</span>
        <span class="n">indexlist</span> <span class="o">=</span> <span class="n">indexlist</span><span class="p">[::</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>  <span class="c1"># order highest to lowest</span>

        <span class="n">matrix</span> <span class="o">=</span> <span class="n">matrix</span><span class="p">[</span><span class="n">indexlist</span><span class="p">][:,</span> <span class="n">indexlist</span><span class="p">]</span>

        <span class="k">return</span> <span class="n">matrix</span></div>

    <span class="k">def</span> <span class="nf">_get_norm_vector</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">matrix</span><span class="p">):</span>
        <span class="sd">&quot;&quot;&quot;</span>
<span class="sd">        Takes a coulomb matrix as input. Returns L2 norm of each row / column in a 1D-array.</span>
<span class="sd">        Args:</span>
<span class="sd">            matrix(np.ndarray): The matrix to sort.</span>

<span class="sd">        Returns:</span>
<span class="sd">            np.ndarray: L2 norm of each row / column.</span>

<span class="sd">        &quot;&quot;&quot;</span>       
        <span class="bp">self</span><span class="o">.</span><span class="n">norm_vector</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">norm</span><span class="p">(</span><span class="n">matrix</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>

        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">norm_vector</span></div>
</pre></div>

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